Higher Order Recurrences for Analytical Functions of Tchebysheff Type

Abstract

One parameter subgroups of the group of hyperbolons of volume one when exploited accurately allow one to define and investigate higher order hyperbolic-trigonometric generalization of corresponding polynomials. In parallel functions of roots of polynomials of any degree are studied as possible extension of symmetric functions considered one hundred twenty six years ago in the inspiring famous lucasian paper.